1. Go to Windows Update, uncheck all but the one update that has failed.
2. In the same window, select Change Settings left side menu, in the drop down box select "Check for updates but let me choose whether to download and install them and then at bottom of window select OK, then at very top left click Back. Do not close the window...
3. Go to Start / Search and type Windows Explorer, Navigate to the following folder
C:\ProgramData\Microsoft\Crypto\RSA
You will see a folder named "S-1-5-18" right click this folder and select rename, rename folder to "S-1-5-18.BAK" click OK, another dialog will appear click continue.
4. Open Windows Update and try installing that update.